Question

In an AC circuit, an alternating voltage, $V=200\sqrt{2}\sin \left(100t\right)$, is connected to a capacitor of capacitance $1\mu F.$ The rms value of the current in the circuit is -

• A. $10\text{mA}$
• B. $30\text{mA}$
• C. $40\text{mA}$
• D. $20\text{mA}$

Answer 1

The correct option is D $20\text{mA}$


Peak current,

$i_0=\frac{V_0}{X_C}=\frac{V_0}{1/\omega C}=\frac{200\sqrt{2}}{\frac{1}{100\times {10}^{-6}}}$

$\Rightarrow i_0=2\sqrt{2}\times {10}^{-2}\text{A}$

Now, rms value of current is,

$i_{rms}=\frac{i_0}{\sqrt{2}}=\frac{2\sqrt{2}\times {10}^{-2}}{\sqrt{2}}=2\times {10}^{-2}\text{A}=20\text{mA}$

Hence, option $\left(D\right)$ is the correct answer.